Definition 5.7 (Sabotage Complexity [1]}) 

The sabotage complexity of a function \(f\) , denoted \(\mathsf {RS}(f)\) , is defined using a concept of sabotaged
inputs \(P_f \subseteq \lbrace 0,1,*\rbrace ^n\)  which is the set of all partial assignments of a function \(f\)  consistent with a \(0-\) input and a \(1-\) input. Let \(P_f^\dagger \)  is defined similarly with the symbol \(*\)  being replaced by \(\dagger \) . Given a (possibly partial) function \(f\) , a partial function \(f_{sab} : P_f \cup P_f^\dagger \mapsto \left\lbrace 0, 1\right\rbrace \)  is defined as \(f_{sab}(x) = 1 \)  if \(x \in P_f\)  and \(f_{sab}(x) = 0 \)  if \(x \in P_f^\dagger \)  (here we view \(P_f,P_f^\dagger \)  as subsets of \(\lbrace 0,1,*,\dagger \rbrace ^n\) ). The sabotage complexity is defined as the randomized query complexity of computing \(f_{sab}\)  i.e. \(\mathsf {RS}(f) = R(f_{sab})\) .

